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Knowledge-Based Variable-Fidelity Optimization of Expensive Objective Functions through Space Mapping

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Computational Intelligence in Expensive Optimization Problems

Part of the book series: Adaptation Learning and Optimization ((ALO,volume 2))

Abstract

The growing complexity of engineering modeling and design problems demands effective strategies for optimization of computationally expensive objective functions. To this end, we focus on knowledge-based, variable-fidelity optimization of expensive functions through a tried and tested, yet still rapidly evolving art called space mapping optimization. Fitting into the arena of surrogatebased optimization, space-mapping optimization is a model-driven optimization process where the model is an iteratively updated surrogate derived from a valid, low-fidelity or physics-based coarse model. Space mapping takes several forms. Here, we present and formulate the original input space mapping concept, as well as the more recent implicit and output space mapping concepts. Corresponding surrogate models are presented, classified, and discussed. A proposed optimization flow is explained. Then we illustrate both input space mapping and implicit space mapping through the space mapping optimization of a simple, technology-free wedgecutting problem. We also present tuning space mapping, a powerful methodology, but one that requires extra engineering knowledge of the problem under investigation. To confirm our work, we select representative examples from the fields of microwave and antenna engineering, including filter and antenna designs.

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Author information

Authors and Affiliations

  1. Engineering Optimization & Modeling Center, School of Science and Engineering, Reykjavik University, Kringlunni 1, IS-103, Reykjavik, Iceland

    Slawomir Koziel

  2. Simulation Optimization Systems Research Laboratory, Department of Electrical and, Computer Engineering, McMaster University, 1280 Main Street West, L8S 4K1, Ontario, Canada

    John W. Bandler

Authors
  1. Slawomir Koziel
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  2. John W. Bandler
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering and Science-Faculty of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-Ku,, 606-8501, Kyoto, Japan

    Yoel Tenne

  2. Advanced Technology Centre, Rolls-Royce Singapore Pte Ltd, 50 Nanyang Avenue, Block N2, Level B3C,Unit 05-08, 639798, Singapore

    Chi-Keong Goh

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Koziel, S., Bandler, J.W. (2010). Knowledge-Based Variable-Fidelity Optimization of Expensive Objective Functions through Space Mapping. In: Tenne, Y., Goh, CK. (eds) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10701-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-10701-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10700-9

  • Online ISBN: 978-3-642-10701-6

  • eBook Packages: EngineeringEngineering (R0)

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